Maybe Paddock was just paranoid, and by removing and disposing of the hard drive, he imagined that he would be "cleaning up after himself" (for lack of a better term). See the short story by Ray Bradbury entitled "The Fruit at the Bottom of the Bowl":
https://en.wikipedia.org/wiki/The_Fruit_at_the_Bottom_of_the_Bowl
He was in the room four days or more, right? He could have removed the drive and tossed it into the hotel trash the same day of the shooting. Perhaps he had an alternate way of booting the laptop. I know nothing of the trials and tribulations of Windows users, but booting a Mac from an external source -- hard drive, USB flashdrive, SD card, etc. -- is a trivial matter. Nuthin' to it.
Nope. If it is true that he was using the cameras as stated, that requires a wireless (or wired) hub, and it requires a computer to collect the data on, either to display or to transmit abroad (as the original story told)... Something was jamming the deal, and if there was only one laptop, that's probably it, which means it was operational till after the shooting.
They had 'eyes on' from the time he was discovered (before the shooting) till after the fact, and he did not exit the room... So if the hdd is discarded, it would be in the local trash (which they would have collected into evidence as a matter of course), or it went down the drain (which would necessitate a usb or cd boot, shattered and flushed), or it went out the window. Not any other options.
And it is not hard to alternatively boot windows. But it is hard to alternatively boot windows as a mini and run software that connects to the camera, and the networking (VPN tunnel through an onion) to send an encrypted and diffused data stream.
Either that thumb would be custom built by a better than average geek, or he knew how himself (either that way, or proficient enough with linux to do the same), or it was a hard drive, with normally loaded and operated software. There aren't any other options, providing they got the story straight.